Two-photon decays and transition form factors of $\pi^0$, $\eta$, and $\eta'$ in large-$N_c$ chiral perturbation theory

TL;DR

This paper calculates the decay processes and transition form factors of neutral pseudoscalar mesons using large-$N_c$ chiral perturbation theory up to NNLO, fitting low-energy constants to experimental data.

Contribution

It provides the first comprehensive NNLO analysis of $P o \gamma^{(*)}\gamma^{(*)}$ decays and form factors within large-$N_c$ chiral perturbation theory, including detailed numerical evaluations.

Findings

Decay widths to real photons are computed.

Transition form factors' slopes and curvatures are provided.

Low-energy constants are fitted to experimental data.

Abstract

We present a calculation of $P\to \gamma^{(\ast)}\gamma^{(\ast)}$ processes, where $P=\pi^0,\ \eta,\ \eta'$, at the one-loop level up to and including next-to-next-to-leading order (NNLO) in large-$N_c$ chiral perturbation theory. The results are numerically evaluated successively at LO, NLO, and NNLO. The appearing low-energy constants are determined through fits to the available experimental data. We investigate the decay widths to real photons, the single-virtual transition form factors, and the widths of $P\to\gamma l^+l^-$, where $l=e,\ \mu$. Furthermore, we provide results for the slopes and curvatures of the transition form factors.